Branching fractions of the decays H_b\to H_c\pi^-\pi^+\pi^- relative to H_b\to H_c\pi^- are presented, where H_b (H_c) represents B^0-bar(D^+), B^- (D^0), B_s^0-bar (D_s^+) and \Lambda_b^0 (\Lambda_c^+). The measurements are performed with the LHCb detector using 35{\rm pb^{-1}} of data collected at \sqrt{s}=7 TeV. The ratios of branching fractions are measured to be B(B^0-bar -\u3e D^+\pi^-\pi^+\pi^-)/ B(B^0-bar -\u3e D^+\pi^-) = 2.38\pm0.11\pm0.21 B(B^- -\u3e D^0\pi^-\pi^+\pi^-) / B(B^- -\u3e D^0\pi^-) = 1.27\pm0.06\pm0.11 B(B_s^0-bar -\u3e D_s^+\pi^-\pi^+\pi^-) / B(B_s^0-bar -\u3e D_s^+\pi^-) = 2.01\pm0.37\pm0.20 B(\Lambda_b^0-\u3e\Lambda_c^+\pi^-\pi^+\pi^-) / B(\Lambda_b^0 -\u3e \Lambda_c^+\pi^-) = 1.43\pm0.16\pm0.13. We also report measurements of partial decay rates of these decays to excited charm hadrons. These results are of comparable or higher precision than existing measurements
